where \(F_{{\rm sink}}\)  is a sink term. On Earth, the sink term represents
a surface drag in the Ekman layer and in the Jovian atmosphere, if
the cells are as deep as the jets [1]}, it might be
Ohmic dissipation [2]}, [3]}, [1]} (i.e., \(F_{{\rm sink}}=\frac{1}{4\pi \bar{\rho }}\overline{\left(\nabla \times \mathbf {B}\right)\times \mathbf {B}},\) 
where \({\rm {\bf B}}\)  is the 3D magnetic field and \(\rho \)  is density).
Eq. 1Note that equation cross-references without a S refer to equations
in the main text., adequate for the upper branch of the cells, results from applying
time-averaging away from the sink layer. This balance leads to meridional
velocities in the directions illustrated in Fig. 2bNote that figure cross-references without a S refer to figures in
the main text.. Alternatively, applying vertical integration cancels the Coriolis
terms in the vertical boundaries of the cell and the relation between
the zonal jets, their eddy source term and the sink term becomes
\(\frac{\partial \bar{U}}{\partial t}=-\frac{\partial }{\partial y}\left(\overline{U^{^{\prime }}V^{^{\prime }}}\right)-\hat{F}_{{\rm sink}}.\) 
